Respuesta :
Answer : The concentration in kilograms of carbon per cubic meter of alloy is, [tex]56.4kg/m^3[/tex]
Explanation :
As we are given that 0.73 wt% carbon in an iron-carbon alloy. That means,
Mass of carbon = 0.73 g = [tex]7.3\times 10^{-4}kg[/tex]
Mass of alloy = 100 g
Now we have to calculate the mass of Fe.
Mass of Fe = Mass of alloy - Mass of C
Mass of Fe = 100 g - 0.73 g
Mass of Fe = 99.27 g
Given:
Density of C = [tex]2.25g/cm^3[/tex]
Density of Fe = [tex]7.87g/cm^3[/tex]
Now we have to calculate the volume of alloy.
Volume of alloy = [tex]\frac{\text{Mass of C}}{\text{Density of C}}+\frac{\text{Mass of Fe}}{\text{Density of Fe}}[/tex]
Volume of alloy = [tex]\frac{0.73g}{2.25g/cm^3}+\frac{99.27g}{7.87g/cm^3}[/tex]
Volume of alloy = [tex]12.94cm^3=12.94\times 10^{-6}m^3[/tex]
Now we have to calculate the concentration in kilograms of carbon per cubic meter of alloy.
[tex]\text{Concentration of carbon}=\frac{\text{Mass of carbon}}{\text{Volume of alloy}}[/tex]
[tex]\text{Concentration of carbon}=\frac{7.3\times 10^{-4}kg}{12.94\times 10^{-6}m^3}=56.4kg/m^3[/tex]
Therefore, the concentration in kilograms of carbon per cubic meter of alloy is, [tex]56.4kg/m^3[/tex]
